{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:JL6KEQ6SQAZSO7EL7MQ2OHZKVS","short_pith_number":"pith:JL6KEQ6S","canonical_record":{"source":{"id":"2111.11175","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2021-11-18T08:07:30Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.data-an"],"title_canon_sha256":"d452dc403a54d845505ba45b85d5386f0ac8a37f11d79dcad3ab5d2cbaaa2c91","abstract_canon_sha256":"25ff78e64031b9f9124e7405d90c0d1b26b47c91afbcdee324487064b59b7f11"},"schema_version":"1.0"},"canonical_sha256":"4afca243d28033277c8bfb21a71f2aac92358d8c54ebe2798cb4204dfffee825","source":{"kind":"arxiv","id":"2111.11175","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.11175","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"arxiv_version","alias_value":"2111.11175v1","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.11175","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"pith_short_12","alias_value":"JL6KEQ6SQAZS","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"pith_short_16","alias_value":"JL6KEQ6SQAZSO7EL","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"pith_short_8","alias_value":"JL6KEQ6S","created_at":"2026-07-05T03:35:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:JL6KEQ6SQAZSO7EL7MQ2OHZKVS","target":"record","payload":{"canonical_record":{"source":{"id":"2111.11175","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2021-11-18T08:07:30Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.data-an"],"title_canon_sha256":"d452dc403a54d845505ba45b85d5386f0ac8a37f11d79dcad3ab5d2cbaaa2c91","abstract_canon_sha256":"25ff78e64031b9f9124e7405d90c0d1b26b47c91afbcdee324487064b59b7f11"},"schema_version":"1.0"},"canonical_sha256":"4afca243d28033277c8bfb21a71f2aac92358d8c54ebe2798cb4204dfffee825","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:35:34.435612Z","signature_b64":"d9TSKqzW8ef0D+6wNZqtCiaWn3oUO4Xsvyh8apHIx9qZExTa4vnO/jsW7EFb4t6Q2VYpPQaScE7mXQ7xZPGlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4afca243d28033277c8bfb21a71f2aac92358d8c54ebe2798cb4204dfffee825","last_reissued_at":"2026-07-05T03:35:34.435235Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:35:34.435235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.11175","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:35:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wcAg5lvKf4YmcBBtuISy2/edrSbAUnCRKnVTkLKtKsB66oxbMf77jHnj/lZrX0t3EyFcpXgLIBUGjbvbCvPMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T12:08:57.924833Z"},"content_sha256":"0ee7df5f9ebceff7a10663e1f51995c5e95bb09bd75330e7a0bb5de80ee3ed34","schema_version":"1.0","event_id":"sha256:0ee7df5f9ebceff7a10663e1f51995c5e95bb09bd75330e7a0bb5de80ee3ed34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:JL6KEQ6SQAZSO7EL7MQ2OHZKVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Generalized Sch\\\"urmann Entropy Estimators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT","physics.data-an"],"primary_cat":"cs.IT","authors_text":"Peter Grassberger","submitted_at":"2021-11-18T08:07:30Z","abstract_excerpt":"We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schuermann, which itself is a generalization of an estimator proposed by myself in arXiv:physics/0307138. For a special set of parameters they are completely free of bias and have a finite variance, something with is widely believed to be impossible. We present also detailed numerical tests where we compare them with other recent estimators and with exact results, and point out a clash with Bayesian estimators for mutual inform"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.11175","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.11175/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:35:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Xfl1d+0OfK7G6Y4MtPbfZHrGi1ISg0RFlz6/WBEWe6kyowTpp9AxRjjzm1ay/lDPXkHy82kKfEqLSUKwSByCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T12:08:57.925402Z"},"content_sha256":"371bc279c82aa1a1c8583e75baa2050178a5eac631cbc2fc04ca323d2e8dca0c","schema_version":"1.0","event_id":"sha256:371bc279c82aa1a1c8583e75baa2050178a5eac631cbc2fc04ca323d2e8dca0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JL6KEQ6SQAZSO7EL7MQ2OHZKVS/bundle.json","state_url":"https://pith.science/pith/JL6KEQ6SQAZSO7EL7MQ2OHZKVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JL6KEQ6SQAZSO7EL7MQ2OHZKVS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-22T12:08:57Z","links":{"resolver":"https://pith.science/pith/JL6KEQ6SQAZSO7EL7MQ2OHZKVS","bundle":"https://pith.science/pith/JL6KEQ6SQAZSO7EL7MQ2OHZKVS/bundle.json","state":"https://pith.science/pith/JL6KEQ6SQAZSO7EL7MQ2OHZKVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JL6KEQ6SQAZSO7EL7MQ2OHZKVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JL6KEQ6SQAZSO7EL7MQ2OHZKVS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"25ff78e64031b9f9124e7405d90c0d1b26b47c91afbcdee324487064b59b7f11","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.data-an"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2021-11-18T08:07:30Z","title_canon_sha256":"d452dc403a54d845505ba45b85d5386f0ac8a37f11d79dcad3ab5d2cbaaa2c91"},"schema_version":"1.0","source":{"id":"2111.11175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.11175","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"arxiv_version","alias_value":"2111.11175v1","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.11175","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"pith_short_12","alias_value":"JL6KEQ6SQAZS","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"pith_short_16","alias_value":"JL6KEQ6SQAZSO7EL","created_at":"2026-07-05T03:35:34Z"},{"alias_kind":"pith_short_8","alias_value":"JL6KEQ6S","created_at":"2026-07-05T03:35:34Z"}],"graph_snapshots":[{"event_id":"sha256:371bc279c82aa1a1c8583e75baa2050178a5eac631cbc2fc04ca323d2e8dca0c","target":"graph","created_at":"2026-07-05T03:35:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.11175/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schuermann, which itself is a generalization of an estimator proposed by myself in arXiv:physics/0307138. For a special set of parameters they are completely free of bias and have a finite variance, something with is widely believed to be impossible. We present also detailed numerical tests where we compare them with other recent estimators and with exact results, and point out a clash with Bayesian estimators for mutual inform","authors_text":"Peter Grassberger","cross_cats":["cond-mat.stat-mech","math.IT","physics.data-an"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2021-11-18T08:07:30Z","title":"On Generalized Sch\\\"urmann Entropy Estimators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.11175","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0ee7df5f9ebceff7a10663e1f51995c5e95bb09bd75330e7a0bb5de80ee3ed34","target":"record","created_at":"2026-07-05T03:35:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"25ff78e64031b9f9124e7405d90c0d1b26b47c91afbcdee324487064b59b7f11","cross_cats_sorted":["cond-mat.stat-mech","math.IT","physics.data-an"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2021-11-18T08:07:30Z","title_canon_sha256":"d452dc403a54d845505ba45b85d5386f0ac8a37f11d79dcad3ab5d2cbaaa2c91"},"schema_version":"1.0","source":{"id":"2111.11175","kind":"arxiv","version":1}},"canonical_sha256":"4afca243d28033277c8bfb21a71f2aac92358d8c54ebe2798cb4204dfffee825","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4afca243d28033277c8bfb21a71f2aac92358d8c54ebe2798cb4204dfffee825","first_computed_at":"2026-07-05T03:35:34.435235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:35:34.435235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d9TSKqzW8ef0D+6wNZqtCiaWn3oUO4Xsvyh8apHIx9qZExTa4vnO/jsW7EFb4t6Q2VYpPQaScE7mXQ7xZPGlBw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:35:34.435612Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.11175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ee7df5f9ebceff7a10663e1f51995c5e95bb09bd75330e7a0bb5de80ee3ed34","sha256:371bc279c82aa1a1c8583e75baa2050178a5eac631cbc2fc04ca323d2e8dca0c"],"state_sha256":"336c59e0dc84b9af40e48394b3eb50de148547b3d676d791f7c7ffc0657ec577"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w5cnJb48t/k55fDyNTt+zkGtrpzv0SMttkvQSy2pZAZYNim299TG5SW7R/cGYJHy0wXdCvqeagQCXiTSQ4/fBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T12:08:57.929354Z","bundle_sha256":"4ba719b44441fe0da3058f9fc17fbf6ab7c2fce5b76f771b2e32903624c1b6b6"}}